Finite Group Databasebeta

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D5×D13×C19⋊C3 #28414839

order14820
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD5×D13×C19⋊C3

Splittings

Fitting, socle, derived, HallC5×C13×C19 ⋊ C22×C3
HallD5×C19×D13 ⋊ C3
HallC5×C13×C19⋊C3 ⋊ C22
HallC13×C19⋊C3 ⋊ C2×D5
HallC5×C19⋊C3 ⋊ C2×D13
HallC13×C19 ⋊ C2×C3×D5
HallC5×C19 ⋊ C2×C3×D13
HallC5×C13 ⋊ C22×C19⋊C3
SylowC19 ⋊ C3×D5×D13
SylowC13 ⋊ C2×D5×C19⋊C3
SylowC5 ⋊ C2×D13×C19⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C13×C19C22×C3
LCSG ▷ C5×C13×C19
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1235

Conjugacy classes & character table

288 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14820, 125);